Calculate usable battery capacity based on rated miles values

[wk057]

First, a bit of a warning to those easily offended by anything negative about Tesla: I've posted several threads about the actual capacities of Tesla battery packs. Raw data with mixed reception. Unfortunately it seems like any time anyone posts a thread that puts Tesla in a negative light most of them tend to get overrun by posts that either aren't on topic or try incessantly to defend Tesla's failing. Bluntly, this thread is not the place for defending Tesla, explaining why they chose to operate as they do, etc. This is about the raw data. Let's gather it, share it, and discuss it logically. If you don't like the data, honestly I don't care. Facts are facts. I don't care if they don't "matter" to you or if you think they don't "matter" to others, and frankly I don't think anyone else cares either. Again, this is about discussing the data and the numbers. Not about how you feel about them. Anyway, sorry about that. The above is my best effort to not have this thread overtaken by nonsense. It's certain to fail, but worth a shot I suppose.

To the facts.

In a previous thread I posted this data about actual pack capacities after gathering data from multiple cars of each variety:

• Original 60 - ~61 kWh total capacity, ~58.5 kWh usable.
• 85/P85/85D/P85D - ~81.5 kWh total capacity, ~77.5 kWh usable
• 90D/P90D - ~85.8 kWh total capacity, 81.8 kWh usable
• Original 70 - ~71.2 kWh total capacity, 68.8 kWh usable
• 75/75D - 75 kWh total capacity, 72.6 kWh usable
• Software limited 60/60D - 62.4 kWh usable
• Software limited 70/70D - 65.9 kWh usable

Edit: For clarification, the larger packs use a 4 kWh bottom lockout and the smaller packs use a 2.4 kWh bottom lockout. This capacity (included in the "total capacity" numbers above) is NOT usable for driving or other purposes.

As it turns out, at or near 100% displayed charge the rated miles (not ideal) * the static rated miles value for the vehicle type/config matches the BMS's reported total usable capacity to within about +/- 1 kWh in nearly all cases I've checked on real cars. The disparity is mainly due to lack of significant figures beyond rated miles, the fact that Tesla rounded the rated miles number to a nearest 5 Wh, and the fact that the car seems to round up on reported rated miles. Also, the rated miles display is not refreshed constantly when the BMS value changes, so there is some latency there. Extrapolating from SoC under 100% results in numbers that are very close, but tend to be off due to other factors.

In general, what you need to calculate capacity are the exact static rated mile values for your type of configuration. And actually, they're pretty simple. Here they are:

• All RWD Cars (non-Performance and Performance): 295 Wh/Rated Mile
• All Pre-refresh Model S Dual Motor, non-Performance: 290 Wh/Rated Mile
• Refresh Model S Dual Motor, non-Performance under 100 kWh: 285 Wh/Rated Mile
• Model X Dual Motor, non-Performance under 100 kWh: 320 Wh/Rated Mile
• Model S Dual Motor, Performance under 100 kWh: 310 Wh/Rated Mile
• Model X Dual Motor, Performance under 100 kWh: 333 Wh/Rated Mile
• Model X Dual Motor, Performance 100 kWh: 342 Wh/Rated Mile

Quick notes: Rated miles are EPA miles. I'm unsure what systems are used in other parts of the world. Internally on the cars everything in miles and uses these numbers then calculates the values for other regions using these as a base.

These are the exact numbers pulled from the Tesla firmware. Rated miles are static Wh/mi. They do not change with driving style or anything else besides the configuration of the car as noted above. The car simply takes the estimated usable energy remaining as reported by the BMS, divides by the appropriate static number above, and displays the value. There is another static value for "ideal" miles, but I haven't bothered to gather it.

For example, at my last 100% charge on my X P90D I reached 245 rated miles. To get kWh usable I look at the list above, pick 333 Wh/Rated mile because it matches my car. Then, I take 245 * 333 to get Wh usable. Then divide by 1000 to get kWh. In this example, I end up with 81.6 kWh usable capacity. The BMS on this car reports 81.7 kWh full usable capacity, so pretty darn close.

For fun, lets use the EPA range numbers from Tesla's website for some examples. All for sale now are refreshed versions, so keep that in mind.

• Model S 60 (s/w limited 75): 210 rated miles * 295 Wh/mi = ~62 kWh usable
• Model S 75: 249 rated miles * 295 Wh/mi = ~73.5 kWh usable
• Model S 60D (s/w limited 75): 218 rated miles * 285 Wh/mi = ~62.1 kWh usable
• Model S 75D: 259 rated miles * 285 Wh/mi = ~73.8 kWh usable
• Model S 90D: 294 rates miles * 285 Wh/mi = ~83.8 kWh usable
• Model S P100D: 315 rated miles * 314 Wh/mi = ~98.9 kWh usable (* Estimated Wh/mi)
• Model X 75D: 237 rated miles * 320 Wh/mi = ~75.8 kWh usable
• Model X 90D: 257 rated miles * 320 Wh/mi = ~82.2 kWh usable
• Model X P100D: 289 rated miles * 342 Wh/mi = ~98.8 kWh usable

As you can see, these numbers actually pretty closely match the capacity values I posted previously. The refresh S 90D appears to make the capacity appear to be a little overrated vs actual capacity, and the X 75D seems to really overstate usable capacity. by over 3 kWh... I'm unsure the reasoning for this. Keep in mind that the rated miles Wh numbers Tesla uses are always rounded to the nearest 5 Wh... which over ~300 miles of rated range is a potential disparity of about +/- 750 Wh before accounting for other factors.

A fun extrapolation: A Model S 100D would have a rated range of 337 miles.

It's also pretty interesting that given the internal static rated miles values the range numbers on Tesla's website pretty closely match actual usable capacity values. However, if you tried to go by the advertised capacity values (60,75,85,90,100, etc) to come up with a rated miles value you'd end up with something totally different in all cases. After taking the 4 or 2.4 kWh unusable portion into account (for the 85,90,100 or 60,70,75 packs respectively), the only cars still sold where advertised capacity doesn't match actual total capacity appears to be the 90. Previous 85 variants would also fall into this category as well. The 60, 75, and 100 actually appear to have packs of at least their advertised total capacities after taking the unusable portions into account. (Only opinion based portion of this post: On that note, perhaps Tesla is trying to actually match their name plate/advertised capacities on newer car variants. Doesn't really help people who own "85"s and "90"s that are short several kWh vs advertised, but, it's a start.)

Anyway, mainly wanted to put out the internal rated miles values so that people can calculate their actual available usable capacities. Should be interesting to see data from more than just the cars I've looked at.

-wk

Edit: Updated some data for 100 kWh variants.

 

[MP3Mike]

Model X 75D: 237 rated miles * 320 Wh/mi = ~75.8 kWh usable

@wk057 This one stands out to me. Does this mean there is almost no anti-bricking buffer, or does the Model X 75kWh pack somehow have more, or different, cells than the Model S 75kWh pack?

 

[wk057]

@wk057 This one stands out to me. Does this mean there is almost no anti-bricking buffer, or does the Model X 75kWh pack somehow have more, or different, cells than the Model S 75kWh pack?

Oh, right, should probably note that one as well along with the S 90D. I'm unsure the reasons for those particular discrepancies, but likely just a result of all of the rounding involved along the way to these numbers on Tesla's side.

 

[woof]

When I had the 2012 S85 (meaning I don't have it anymore, so I cannot check), I swear the "rated" number (as calculated by the dashed line marked "rated" on the energy graph) was 303 Wh/mi. Am I mistaken? Does the "rated" line on the energy graph not match the numbers above? Or was the original S different?

 

[wk057]

When I had the 2012 S85 (meaning I don't have it anymore, so I cannot check), I swear the "rated" number (as calculated by the dashed line marked "rated" on the energy graph) was 303 Wh/mi. Am I mistaken? Does the "rated" line on the energy graph not match the numbers above? Or was the original S different?

As far as I can tell in firmwares as far back as I have (4.0 or something) the number has always been 295 Wh/mi on the RWD S. It's certainly possible behavior was different before then, but I don't have that data.

 

[spottyq]

Thanks for the informative, to-the-point post !

 

[hacer]

So the software limited refreshed 70D has 240 RM initial full range. Using your formula that gives 240 * 0.285 = 68.4 kWh which is a lot higher than the 65.9 that you measured from the BMS system.

I've always wondered if there wasn't something wrong with the way the software manages the refreshed 70D.

 

[scaesare]

As far as I can tell in firmwares as far back as I have (4.0 or something) the number has always been 295 Wh/mi on the RWD S. It's certainly possible behavior was different before then, but I don't have that data.

Interesting. On my early '13 S85, my graph rated line is right at about 275Wh/mi, and if I maintain that average for a trip, I nail rated mileage pretty much exactly. I wonder where the discrepancy is...

Good stuff, thanks wk...

 

[randvegeta]

As far as I can tell in firmwares as far back as I have (4.0 or something) the number has always been 295 Wh/mi on the RWD S. It's certainly possible behavior was different before then, but I don't have that data.

I have only owned my 2014 S 60 for 3 weeks or so but my rates miles are definitely not static. When I first got the car, it was 188wh/km, which works out to be around 313wh/m. And now its hit 191wh/km. How can this be?

 

[wk057]

I have only owned my 2014 S 60 for 3 weeks or so but my rates miles are definitely not static. When I first got the car, it was 188wh/km, which works out to be around 313wh/m. And now its hit 191wh/km. How can this be?

The value used per rated mile doesn't change. Your driving can effect actual efficiency, obviously. And as pack degrades and you get less rated miles per charge the value per mile is still the same.

 

[Missile Toad]

@wk057 thanks for your sleuthing. Good figures to use in my number-crunching.

So I used your Firmware numbers on my pre-refresh 70D, namely 290 Wh/mi with the EPA 240 miles to get 69.9 kWhr. I've been systematically measuring the kWhr deltas that co-occur with 40 RM deltas (1/6 of EPA range) to see how the RM declining value comports with the tally of kWh used during the trip. Each measurement is taken while the car is in motion at the transition from RM to RM-1, and then recorded again at the transition RM-40 to RM-41. I try, but can't be sure, that my speed is identical at each measurement (which will introduce errors because of the kinetic energy in the car was from the battery to start with). My data, so far, shows 10.7 kW per 40 RM, with some variation +- 0.2 kW/40RM.

This results in RM declining much faster than the presumed USABLE kWhours do. Only 6x10.7=64.2 kWhr are gone when 240 RM drops to 0 RM. So, in theory, a 0 RM leaves about 5.7 kW hidden, in the battery, but usable to me. This works out to be about 19 more miles of 'go'.

Warning: anyone who wants to drive into negative RM should be aware that at each parking of the car, vampire drain can occur, where the main battery delivers some unknown W-hours to the 12V battery ... which will shrink those extra 'go' miles.

 

[TLej]

Pre-refresh S90D, delivered Dec 29/15. 24,000 +/- km at this point. Most recent 100% charge was 442 rated kilometres. Rated figure is 180 Wh/km. 180*442 = 79,560 Wh, or 79.6 kWh. This is about 4.2 kWh shy of your number above, some of which will be degradation.

 

[AWDtsla]

This results in RM declining much faster than the presumed USABLE kWhours do.

I think this is just the trip meter not working right, the numbers it produces are not even self-consistent. It would be nice to get some analysis of it @wk057. I believe someone, maybe you, pointed out the problem with it was it was integrating the energy usage itself, and was prone to missing samples thereby continuously undercounting the used energy to some degree.

 

[DB 2]

The car simply takes the estimated usable energy remaining as reported by the BMS, divides by the appropriate static number above, and displays the value.

Is this true at all SOC levels or only at or near 100%. In other words, if BMS usable energy remaining is 1/4 of BMS usable energy when full, will the instrument cluster show rated miles remaining as 1/4 of what it showed when you completed a 100% charge.

 

[wk057]

Pre-refresh S90D, delivered Dec 29/15. 24,000 +/- km at this point. Most recent 100% charge was 442 rated kilometres. Rated figure is 180 Wh/km. 180*442 = 79,560 Wh, or 79.6 kWh. This is about 4.2 kWh shy of your number above, some of which will be degradation.

As pointed out in my post, I don't know what numbers are used for rated kilometers in other regions. Unless you have a setting that gives you the EPA-type rated miles equivalent. I haven't dived into investigating for other regions since the conversions used are scattered throughout the code it seems.

@wk057 thanks for your sleuthing. Good figures to use in my number-crunching.

So I used your Firmware numbers on my pre-refresh 70D, namely 290 Wh/mi with the EPA 240 miles to get 69.9 kWhr. I've been systematically measuring the kWhr deltas that co-occur with 40 RM deltas (1/6 of EPA range) to see how the RM declining value comports with the tally of kWh used during the trip. Each measurement is taken while the car is in motion at the transition from RM to RM-1, and then recorded again at the transition RM-40 to RM-41. I try, but can't be sure, that my speed is identical at each measurement (which will introduce errors because of the kinetic energy in the car was from the battery to start with). My data, so far, shows 10.7 kW per 40 RM, with some variation +- 0.2 kW/40RM.

This results in RM declining much faster than the presumed USABLE kWhours do. Only 6x10.7=64.2 kWhr are gone when 240 RM drops to 0 RM. So, in theory, a 0 RM leaves about 5.7 kW hidden, in the battery, but usable to me. This works out to be about 19 more miles of 'go'.

Warning: anyone who wants to drive into negative RM should be aware that at each parking of the car, vampire drain can occur, where the main battery delivers some unknown W-hours to the 12V battery ... which will shrink those extra 'go' miles.

I think this is just the trip meter not working right, the numbers it produces are not even self-consistent. It would be nice to get some analysis of it @wk057. I believe someone, maybe you, pointed out the problem with it was it was integrating the energy usage itself, and was prone to missing samples thereby continuously undercounting the used energy to some degree.

Addressing both of the above, first I only was able to investigate the usable capacity one two cars with non-software limited 70 packs. However, the physical configuration of those packs (14 modules similar to the "85" type packs) would seem to match those conclusions, which would calculate out to ~69 kWh usable. I also only have information about the software limited 75->70 packs from two cars, both of which reported the number I gave earlier. It's possible Tesla fixed that error since I acquired the data, but I'm unsure.

Additionally, the trip meters are handled entirely by the MCU (CID). They rely on just watching the BMS data and constantly computing the used power. I've found it to almost always underestimate power usage due to missing small amounts of data. You can prove this by rebooting the CID while driving and checking the trip meters. You'll notice they don't update for some time during the reboot.

Further, probably most importantly, and I have said this many times before.... THERE IS NO HIDDEN POWER AFTER 0%. NONE. ZIP. NADA. The BMS is continuously measuring energy usage to calculate an accurate capacity, and it does this pretty well in most situations unless the current shunt calibration is way off. When the car reaches 0% it can compare actual data with expected voltages for the current pack temp, among other things, and determine if it's safe to continue to draw the pack. There is no way this calibration will be off by any appreciable amount in the newer firmware, and usually won't be off by anything at all. When the pack reaches the cut off voltage, you can't drive anymore. Simple as that. If you're lucky your calibration is off by 1 or 2 rated miles, but that's a best case scenario.

So everyone PLEASE stop spreading information suggesting that you can drive below 0. You can not, and you should not try to.

Is this true at all SOC levels or only at or near 100%. In other words, if BMS usable energy remaining is 1/4 of BMS usable energy when full, will the instrument cluster show rated miles remaining as 1/4 of what it showed when you completed a 100% charge.

For the most part this is correct, however as mentioned in my post the updating of displayed rated miles is not as quick as the actual BMS values. For example, rated miles may tick down more quickly than expected when you're in a situation where you regen a lot. Then they might tick down slower long after the regen area was over. Long story short, while not at or near 100% SoC there is a little bit of hysteresis happening with the updating of the actual displayed value of rated miles which can cause it to be a little bit off of the actual reported usable capacity.

 

[TLej]

As pointed out in my post, I don't know what numbers are used for rated kilometers in other regions. Unless you have a setting that gives you the EPA-type rated miles equivalent. I haven't dived into investigating for other regions since the conversions used are scattered throughout the code it seems.

The energy screen tells you what the rating is. Solid line just under 200 below. If my recent average was closer to 200, you'd see the number of what the rating is if memory serves. It's been a while since I was anywhere close to it. Also, taking your figures for Wh/mi and dividing by 1.6 gives 181, close enough for rock'n'roll.

 

[f-stop]

[...] For example, at my last 100% charge on my X P90D I reached 245 rated miles. To get kWh usable I look at the list above, pick 333 Wh/Rated mile because it matches my car. Then, I take 245 * 333 to get Wh usable. Then divide by 1000 to get kWh. In this example, I end up with 81.6 kWh usable capacity. The BMS on this car reports 81.7 kWh full usable capacity, so pretty darn close.[...]

great post, very informative. one question, regarding range mode
I notice if I turn on range mode, the displayed rated miles goes up slightly. I assume in your example calculation the rated miles number (245mi) is with range mode off - So I assume the effect of turning range mode on is to simply adjust(reduce) the static rated mile constant by a bit, to reflect the lower energy usage of the car with range mode on. Is that correct?

for example, my pre-refresh 70D most recent range charge showed 384 rated km at 100% (so, 238.6mi) x 290Wh/mi /1000 = 69.2kWhr usable. After that same charge, I turned on range mode and the display changed to 388km rated (so 241.1mi).
Assuming the same 69.2kWhr usable, this tells me range mode constant would be 287Wh/mi instead of 290 (about 1% reduction in energy used, for range mode)

BTW, when new, my car's 100% rated range (range mode off) was 386km = 239.9mi -> x290/1000 = 69.6kWhr usable. If my numbers are correct, seems pretty close to the advertised 70kWh, and also only about 0.6% reduction in the ~13.5months since delivery.

 

[AWDtsla]

I notice if I turn on range mode, the displayed rated miles goes up slightly.

I've seen this in youtube, but have never actually observed it on my own car. Is your pack very cold when you see this?

 

[f-stop]

I've seen this in youtube, but have never actually observed it on my own car. Is your pack very cold when you see this?

I don't think a cold pack has anything to do with it, I've noticed it each time I've turned on range mode before heading out on a road trip - and this has been at various times of the year (e.g. June, Sept, Oct...).

That said, most instances were sometime in the a.m, after car sitting in the (unheated) garage overnight, since I was leaving on a trip at beginning of the day. but none of those times would have been particularly cold. Likewise every time I've turned off range mode, I've noticed the rated km displayed go down by a few km. I expect if I go out to my car now and turn on range mode without doing anything else, the displayed rated km will go up slightly... (but I won't do that now, it's definitely cold outside right now!)

 

[stevezzzz]

When I had the 2012 S85 (meaning I don't have it anymore, so I cannot check), I swear the "rated" number (as calculated by the dashed line marked "rated" on the energy graph) was 303 Wh/mi. Am I mistaken? Does the "rated" line on the energy graph not match the numbers above? Or was the original S different?

I recall the same 303 Wh/mi value for achieving Rated range on my very early Sig S85 (delivered in September, 2012). I cross-checked the Trip meter's average energy consumption against the Energy graph's 30-mile averager, on several occasions, and it always came in at 303 or 302 Wh/mi when the predicted range remaining lined up with the Rated range remaining. I'll have to dig back through my photos to see if I can document this: I used to be fairly obsessive about taking snapshots of the Energy graph and Trip meters when on road trips.

This higher consumption value (303 vs 295) may have to do with the higher curb weight of early Model S compared to the cars that rolled off the line a year or two later, after Tesla completed a weight reduction program for the S.